How to Find the 't' Value in Integral Calculus?

[temp]

hello
commonly we have:
$$\int^t_0 \ dx=M$$

"M" is a specific number (the result of integal)

my question:
having value of "M", how we can find the "t" value

 

[VietDao29]

hello
commonly we have:
$$\int^t_0 \ dx=M$$

"M" is a specific number (the result of integal)

my question:
having value of "M", how we can find the "t" value

This sounds much like homework to me. >"<

What have you done? Have you tried anything?

Ok, I'll give you some hints then:

1. What is the anti-derivative of: $$\int dx = ?$$

2. What is : $$\int_0 ^ t dx = ?$$ in terms of t?

3. What is the relation between t, and M?

 

[cristo]

hello
commonly we have:
$$\int^t_0 \ dx=M$$

"M" is a specific number (the result of integal)

my question:
having value of "M", how we can find the "t" value

In case this isn't homework and is a question from curiosity: In general, there is a function being integrated; $$\int^t_0 f(x) dx=M$$. In which case, the answer to your question is "only if we know the function, f."

 

[temp]

i know the function f(x)
suppose that f(x) is x

$$\int^t_0 x dx=M$$

 

[HallsofIvy]

What IS the integral (anti-derivative) of x? Do the integration on the left, set it equal to M and solve the equation for t.

In the very simple case, you started with, $\int_0^t dx$, the anti-derivative of the constant 1 is just x
[tex]\int_0^t dx= x\right|_0^t= t[/itex]
In that case, whatever number M is, you have t= M. For the case of
$$\int_0^t x dx= M$$
it is almost as simple.